A method for constructing a high rise building having a core and a residence space around the core, the method including (a) installing a steel-frame pillar on a shaft portion of the core; (b) connecting a girder to the steel-frame pillar, the girder includes an anchor-connecting member to which a steel-frame beam is connected, a portion of the anchor-connecting member being buried in a core wall; (a) assembling the steel-frame beam on the anchor-connecting member; (d) arranging reinforcing bars in a deck plate or a slab type mold installed on the steel-frame beam, and in the core wall; and (e) applying a slab concrete and a core concrete simultaneously or in this order. The quality of the core and slab structure is improved, while providing the construction safety and saving the construction costs.